Observables of the generalized 2D Yang-Mills theories on arbitrary surfaces: a path integral approach

TL;DR

This paper employs the path integral method to compute the partition function and generating functional of generalized 2D Yang-Mills theories on various surfaces, including orientable and nonorientable ones.

Contribution

It provides a comprehensive calculation of these functionals for arbitrary surfaces using a path integral approach, extending previous results to more general geometries.

Findings

Partition function derived for arbitrary surfaces.

Generating functional of field strengths obtained.

Method applicable to both orientable and nonorientable surfaces.

Abstract

Using the path integral method, we calculate the partition function and the generating functional (of the field strengths) of the generalized 2D Yang-Mills theories in the Schwinger--Fock gauge. Our calculation is done for arbitrary 2D orientable, and also nonorientable surfaces.